Slide-rule.



PATLNTLD MAR. 3, 190s.

y P. F; NICKEL.y

SLIDE RULE. APP-LOATION FILED DBO. 28,11906.

INVENTOR 4 SHEETS--SHEET 1.

#QM/ ATTRNEY No. 880,907. P AIENTBD MAR. 3, 1908 F. F. NICKEL.

SLIDE RULE.

APPLIGATION FILED DEC.28, 1906.

4 SHEETS-"SHEET 2.

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,UNiTED sTATEs PATENT oEEioE. f

FRANZ E. NICKEL, 'or EAsT ORANGE, NEW JERSEY.

East Orange', inthe county of Essex and.

State of New Jersey, have invented a certain -new and useful Improvement in Slide-Rules,

of which the following is a specification.

My invention -relates to the so-called slide rules, and it has for its object a rule of this character by-means of which certain problems which with the-ordinary form of slide rule would require several settings of 'the slide, may be solved with but a single setting. 1 I refer particularly to such problems as the determination ofthe mean effective pressure in a steam cylinder when tlie initial pressure and the ratio of ex ansion are given: orv the determination of t e mean effective pressure in an air compressor when the initial pressure'and'the ratio of compression are given.

' Further, my invention comprehends a rule of this character., which will not in any way decrease the scope and application of the present forms of slide rules, but gives additional usefulness thereto. w l

For this purpose my-invention consists in the `novel ,arrangement of certain additional scales4 .of graduations to be used in conjunction withthe present form of slide rules, or with specially constructed slide rules.

' The nature of my invention will best be \understood in connectionwith the. accompanying. drawin s in which-l Figure 1 isa `an view of a runnerless form of slide rule; i ig. 2 is a view of the reverse side of the slide graduated accordinl to my invention. Fig. 3`is a similar view o the reverseside of the slide graduated laccording to my invention and provided 'also with the usual scales. Figs. 4 and 5 are views of the reverse side of the rule. 'Fig 6 is an end view of the rule. Fig. 7 isa plan view of lanother form of slide rule -and provided witlia runner. Fig. 8-is a view ofthe reverse side of the slide used in conjunction with the rule shown in Fig. 7 and provided with the additional'"` raduations.

rule.

As shown in the drawings, the main iece `of my improved slide rule consists o two fixed para el bars l() and 11 .connected by a cross-piece 12 the under f ace of which is vadapted for a table of constants Orforrnulas.

SLIDE-RULE Specification of Letters atent. Patented March 3,1908. Appleman med vDecember 2s, isos. serial No. starmi.`

edges with longitudinal grooves in which is guided a slide 13 having longitudinal tongues fitting the said grooves. y14 represents an glassorother transparent material, having a distinct line marked across the underside oi' its face. 1 Notches 15 and 16 are provided respectively at the left and right hand ends of the main piece upon -the under side and are provided with the-guide marks 17, 18, and 19, 20 respectively The fixed bari() is provided with two logarithmic scales marked 1, the one progressing from the left handend to the median point of the graduated length of the rule, and the other from the said median 1 1 is provided with a single logarithmic scale to the right hand end of the bar.

At the upper edge of the slide 13 are two logarithmic scales marked 2 in juxtaposition left hand end. to the said median point, Vand fthe other from the median point to the right hand end of said slide. At the lower edge are two logarithmic scalesvv marked 4 similar to those at the upper edge,- `on the scale 2 as shown in Fig. 1 progressing from the left hand end to the median point, and from the median point to the right hand end of the slide in juxtaposition to the scale 2; or a single logarithmic scale progressin from the left hand end lto the right hand en in juxtaposition to the scale 3 as shown in Fig. 7. The reverse side ofthe slide is usually provided with three scales S, T and L, the first at theupper edge being a logarithmic scale progressingkrom left to right and used in finding the sines of angles and the second at the lower edge' progressing from left `to right as in Fig. 8, or from right to left as in Fig. 3 and used in finding the tangents of angles.- The third lscale is generali provided in the center of the slide and is ivided into equal parts progressing from right to left and used, 1n -inding the logarithms vor numbers. These scales are read in conjunction with the marks 19,. 1 8', and 20 respectively .in the `notches 15 and. 16. To determine the logarithiiiy of a number the left hand index of scale 4 is set-over the4 number on scale 3 and the lo `aritlim is read over the mark 20 in Athe right and notch 16.' It will be noted that in determining the logarithms of num- The bars 10and 11 are provided at their inner ordinary runner provided with a piece ofA to the scales 1, the one progressing romthe point to the right hand end. The fixed bar marked 3v progressing from the lefthandend bers from 1 toi 3.16 less than one-half of the slide projects at the right hand end; whereas, in determining the logarithm of numbers from 3.16` t 10 more than one-half of the 'which the runner 14 is required;v or preferably on the reverse side of the slide A13 as shown in Figs. 2, 3, 8 and 9, and preferably below lthe longitudinal center line of the slide, the said scale in either case occupying not more than one-half of the graduatedA length of the rulc. This scale progresses in the former case from the median point toward the left 'hand end, and in the latter from the left hand end toward 'the median point. f

My invention provides further for a second additional logarithmic scale A (used to determine the mean effective pressure in the air compressor) either on the upper edge of the b ar 10 as 'shown in Figs. 13 and 14; or preferably on the reverse side of the slide 13 as shown in Figs. 2, 3, 8 and 10 and prefersai scale in either case occupying not more than one-half the graduated lengthof the rule. "This scale progresses in the former ca se from the median point toward the right handend, and in the latter from the right hand end toward the median point. The

scale R begins with- 1 whichrcoincides withv the line `10 of the scale of logarithms in the form of rule shown in Figs. 1,7, 11v and- 12 and progresses toward the right up to 40, thus representing ratios of expansion from 1 to 40 or as in the form shown in Figs. 13 and 14,v

the 'division 1 is in the same vertical line with the medianpoint and progresses toward the left, theI transfer to the other scales being made with the runner 14. In the samemanner the scale-A is arranged to represent the ratios of compression from 2.4 to 40, the progression being as previously explained. Additional figures are also provided to cover ratios of compression lower than 2.4.

Reverting now to the rst mentioned problem, viz: to find the mean effective steam pressure when the initial pressure and the ratio ofjexpans'ion are given, itis necessary to divide this problem into three A:steps or operations. As. eduction cannot be performed on theslide-rule, the back pressure must'rst beseparated, whichv leaves the mean pressure to be calculated. This-mean I pressure can be resolvedi'into two factors-' the initial pressure, and a coe'iiicie'nt'repre-` senting the mean pressure per pound of ini-l tial pressure.

coefficient.'

ably above the longitudinal center line, the

In' connectioii'with the second mentioned problem, viz: to find the mean effective pres sure when the initial pressure and the ratio of compression are'given, the back pressure need not be separated (it beingtheinitial pressure) and ,Itllerefore can be included in the e initial pressure W' l therefore ive the mean effective pressure directly. he scales R and A are logarithmic scales representing these coeflicients forvarious ratlos of expansion and compression as explained, and are arranged to occupcy not more than onehalf of t e graduate length of the'rule.- Therefore for any setting, not more than onehalfof the slide projects beyond the rule.

roduct of coefficient and The coefficient may therefore be located on the scale opposite the median point of slide when the s ide' 13 is properly set and without further setting can be multiplied by any number (representing the initial pressure).

If therefore the slide13 be set so that the ratio of expansion on scale R coincides with the mark 17, as in Fig. 9; or as in Fig. 13, so that the median point of the slide is in the s ame vertical line with the given ratio of expansion, the coefficient may be read on scale 1. Then, `over the initial pressure found on scale 2, the mean pressure in the case of exparisien, or the mean effective pressure in the case of compression, may beread without further setting on scale 1. This is illustrated in Figs. 9 to 14, Figs. 9 to 12 illustrating the v application with the additional scales R and A on the reverse side .of the slide 13 g and Figs. 13 and 14 the application with the additional scales on the upper edge of the bar 10. In the first case a ratio of expansion of `4' isassumed and the number`4 of scale R on the reverse side of the slide 13 is set to coincide withthe mark 17 on the notch 15, see Fig. 9. The median point of the slide 13 will then be found to be under the point 0.1597 of .scale 1 and the rule is thereby set for any multiplication, so that it is only necessary to read off the answer of 71.6 on scale 1 for an initial pressure of say 120 lbs. absolute over-the point 120 on scale 2. In the same manner for an assumed ratio of compression of 6, the number 6 of scale A on the reverse side of the slide 13 is set to coincide with the mark 20 of notch 16 and the answer 34.5 determined by multiplying the coefficient 2.35 by the assumed initial pressure 14.7 lbs. absolute. y

In the form of slide rule illustrated in Figs. 13 and-14 the operation is substantially similar, reference being had to Fi S513 and 14. The exception is that the coe cient is determined on sc ale 1 by setting the median point of the slide 13 in the same vertical line as the given number ofexpansions or com ressions represented bythe scales R or 'A on t e upper edge of bar 10, the line of the runner 14 being used to make this adjustment or transfer.`

This lgives the coefficient on scale 1 over the l median point of scale 2, and the multi lieation by initial pressure is erformed as a ove.

i graduated to represent terms of other similar ormulas.

I 'claim:- A 1. In a slide rule consisting of a main piece havin an u per and a lower fixed bar anda rithmic scales upon the upper bar, the one progressing from the left hand end to-the me ian pointof the graduated length of the rule and the other from said median point` to the right hand end; a single logarithmic scale upon the lower bar, rogressing from the left hand end to the. rigli rithmic scales upon the slideat its upper edge the one progressing from the left hand end to the median point 'and the other from said median point to th'e right hand end; two logarithmic scales upon the silde at its lower edgef the one progressing from the left hand end to the median point and the other from said mey c dian point to the right-hand end; a lo arithmic scale upon the reverse side of the s ide atits upper edge, progressing from the left hand end to the right hand, end; a logarithmic scale u on the reverse sideof the slide at its lower e ge, rogressing from the right handgend to the le t hand end; a'scale upon the reverse side of the slide between said scales on the reverse side, pro ressin f roinright to left; and one or more ad itiona logarithmic scales each occupyin not more than one-half of the graduated ength of the rule. y

2. In a slide rule, consistingV of a main piece having au upper and a lower fixed bar anda movable slide between saidgbars: two loga.

ritliinic scales upon the upper bar, the one progressinor from the left hand end to the me( ian pozint of the graduated length ofthe rule and the other from said median point to the right hand end; a single logarithmic scale upon the lower bar, progressing from the i left hand end to the right h and end 5 two logarithniic scales upon the slide atits upper edge,

the one progressing from the left hand endA to the median point and the other fronisaid median point to the rightliand end two logarithmie scales upon the slide at its lower edge,

the one rogressingfrom the left hand end tov the rhe ian point and the other 'from said median point to' the right hand end a logai rithmic scale upon the reverse side of the slide at its upper edge, .progressing from the left hand end to the right hand end, a 'logarithmic scale upon the reverse side of the slide'at its lower edge, progressing from the right hand end to the left han`d end; 'a scale upon the reverse side of the slide between saidscales on' the reverse side, progressing' froml right to left; and anl additional logarith l said rule progressingfrom the left hand end of said slide to the median uated length of said rule. Y

3. In a lslide rule, consisting of a main piece having an upper and alower iixed bar and a movable slide between said bars: two logalrithmic'A scales upon the upper bar, the one pro ressing from thek left hand' end to the me( ian pointV ofthe graduated length ofthe ruleand the other from said median point to Inova le sli .e between said bars: two loga- .-l the right hand end; a single logarithmic scale upon the lower bar, progressing'rom the left hand end to the right hand end; two logarithrnie' scales upon the slidel at its upperpoint ofthe grad-rv n'iic scale on the reverse side of the slide of soy edge, the one progressing from the left hand i end to the median point and the' other from said median point tothe right hand end; two

logarithmic scales upon the slide at'tslower s edge,;tlie one progressing from the left hand end to the median point and the other from said median point to the right hand end; a

logarithmic scale upon the reverse side of the slide at .its u per edge, progressinglfrom the left hand en to the right hand end a logarithinic scale upon the reverse side of the slide at its lower edge, progressing from the right handend to the left hand end; a scale upon the-'reverse side of the slide between said scales on the reverse side, rogressing from right to left; an additional ogarithmic scale `on the reverse side of the slide of said rule progressing from theleft hand end of said i slide` to the median point of the graduated length of saidI rule; and a second additional logarithmic scale likewise on the reverseside of said slide but progressing from the right handvend of said slide to: the said median point, i

4. In slide rule, consisting of a main piece having an upper and a lower fixed bar and a movables'lidebetweensaid bars: two logarithmicv scales upon the upper bar,- the one progressing from the left hand end t'o the inedian point of the graduated length of the rule and the other lfrom said medianl point to the right hand end; a single logarithmic scale upon the lower bar, progressing from the left.

hand end to the right hand end; two logarithniic scales upon the slide at its 'upper Vedge', the one progressing from the leftliand end to the median pointv and the other from said median point-tio the right hand end; two, vlogarithmic scales upon the slide at its Ilower edge, thel one progressing from the left hand end to the median point and the other from said median point to the right handend; a logarithmic scale upon the reverse side of the slide at its upperA edge, progressing frorn the left hand end to the, right hand end; a logarithmic scale' upon the reverse side of the slide at its lower edge, progressing from the right hand end to the left hand end; a spele upon the. reverse side of the slide of said rule progressing directly below the longitudinal center line of said slide from the right hand end of the slide to the median point of the graduated length of the rule, and directly above the said longitudinal center line from the said median point to the left hand end of said slide; an additional logarithrnic scale on the reverse side of the slide of said rule progressing directly below the longitudinal center line of said slide from the left hand end of the slide to the median point of the graduated length of the rule, and a second additional logarithmic scale on the re verse side of the said slide progressin directly above. the said longitudinal center line from 15 the right hand end of said slide to the said median point.

Signed at New York in the county of New York and State of New York this 26th day of December A. D. 1906.

/ FRANZ F. NICKEL. Witnesses:

A. FABER DU FAUR,` FREDK. F. SoHUL'rz. 

